1. Field of the Invention
The invention is in the area of determination of Nuclear Magnetic Resonance properties of materials. Specifically, the invention is related to modifying the temporal shape of excitation pulses used in measurement procedures in downhole wellbore logging techniques.
2. Description of the Related Art
NMR methods are based on the well-understood properties of nuclear spin moments when they are subjected to a static external magnetic field along with an oscillating external magnetic field. It is known that in the absence of a magnetic field, spins tend to orient themselves in random directions. In the presence of only a static magnetic field, these individual spins tend to align themselves along the direction of the applied field. This alignment gives rise to an overall magnetization, referred to as the bulk magnetization vector. When the external field is removed, the spins resume their random orientation, and the bulk magnetization vector falls to zero.
Typical NMR methods determine properties of the material by observing how applied RF magnetic fields affect the spin vectors. In current methods, spins are first aligned via the application of a static external magnetic field, causing a magnetization. In well logging, this magnetic field is typically provided by a permanent magnet. Once equilibrium magnetization has been reached, a single RF magnetic pulse is applied perpendicular to the static field that aligns the spins generally in the plane perpendicular to this applied field and generally perpendicular to both the static and RF fields. This pulse tips the magnetization into a direction perpendicular to the static magnetic field and is referred to as a 90 pulse. After the application and removal of a 90 RF magnetic pulse, the spins exhibit a precession around the direction of the static field with a frequency known as the Larmor frequency. The Larmor frequency is given by xcfx890=xcex3B0, where xcex3 is the gyromagnetic ratio and B0 is the strength of the applied constant field. This precessing magnetization induces a signal in a surrounding coil. This is the NMR signal.
After the application and removal of a 90 RF magnetic pulse, the spins tend to re-align with the static magnetic field. The re-orientation along this direction is characterized by a time constant known as the spin-lattice relaxation time, T1.
Typically, the effective static magnetic field is inhomogeneous throughout the formation. As a result, each spin vector tends to precess at slightly different rates, according to its local magnetic field. The phase between the vectors, originally nearly zero at the moment the RF magnetic field is removed, diffuses as some vectors spin faster and some spin slower. The diffusion of the phase leads to a reduction of the component of the bulk magnetization in the plane perpendicular to the applied field. This process is known as dephasing. This component reduction is known as the free induction decay (FID) and is characterized by its time constant, T2*. The dephasing can be recovered partly as long as the underlying cause, the local spatial variation of the magnetic field, is static. Recovering the phase is done by using one or more refocusing pulses and leads to the formation of one or more spin echoes. The decay of these echoes is characterized by its time constant T2.
To observe the values for these time constants and in particular of T2, the practitioner often applies a sequence of RF magnetic pulses. A sequence of pulses that is used widely in current methods is known as the Carr-Purcell-Meiboom-Gill (CPMG) sequence. In this sequence, the first pulse is a 90xc2x0 pulse, which aligns the spins generally perpendicular to the applied static magnetic field. Subsequent pulses have twice the duration of the first pulse, and as a result are able to flip each spin vector a full 180xc2x0 from the direction it had immediately prior to the application of the pulse. A 180xc2x0 pulse is typically applied during a dephasing stage of the spin echoes. After the pulse is removed, the order of the spins is reversed, with the slowly precessing spins spatially in front of the faster precessing spins. The phase between the spin vectors, which was previously diffusing, now is converging back to zero. At convergence, the spin vectors are generally aligned in a common direction again, and the bulk magnetization vector reaches a maximum value, creating a magnetic pulse known as a spin echo. The spin echo induces a voltage in a receiver coil, which is measured through the electronic assembly attached to the coil.
The CPMG sequence can be expressed as
TWxe2x88x9290xe2x88x92(txe2x88x92180xe2x88x92txe2x88x92echo)nxe2x80x83xe2x80x83(1) 
where TW is a wait time, 90 is an excitation pulse having a tipping angle of 90xc2x0, and 180 is a 180xc2x0 refocusing pulse. This gives a sequence of n echo signals.
The shape of the CPMG pulse can have enormous impact on the amount of power consumption and efficiency of the well-logging process. Current methods commonly use a rectangular pulse to flip the orientations of the nuclear spins. Due to the Fourier series relation between time and frequency, the shape of this pulse in the frequency domain is that of a sinc function (sinxcfx89t/xcfx89t). For several reasons, the rectangular pulse therefore is not an ideal excitation profile. Firstly, the corresponding function in the frequency domain contains many side lobes of alternating sign. Thus, substantial power is consumed by frequencies of the side lobes rather than by the desired central excitation frequency. Also, pulse power increases with the square of the required excitation bandwidth. This is because the pulse amplitude must be inversely proportional to the pulse temporal length of the RF pulse if the spin tip angle is to stay constant, say 90xc2x0. Due to a high level of coherency at time zero and destructive interference at later times, the pulse is of short duration and high power.
Co-pending U.S. patent application Ser. No. 09/606,998 of Beard et al having the same assignee as the present application teaches the use of pulse shaping in a gradient NMR logging tool for reducing interference between frequencies used in a multifrequency NMR acquisition method. This is desirable in a multifrequency logging instrument to avoid interference between the sidelobes of pulses at one acquisition frequency with the center frequency of an adjacent frequency band. The pulse shaping described by Beard deals only with the shape of the excitation and refocusing pulses.
Pulse shaping has been discussed in Guan for the problem of NMR solvent suppression. In NMR solvent suppression it is desirable to suppress the solvent signal when studying a small concentration of a substance of interest in a solvent. To suppress the solvent and only see the wanted NMR signal, Guan uses an RF pulse which has a non-contiguous frequency spectrum, i.e. a spectrum with a notch at the solvent resonance frequency. U.S. Pat. No. 5,814,987 to Smith et al teaches the use of pulse shaping for Nuclear Quadrupole Resonance (NQR) testing.
In a preferred embodiment of the invention, a static magnetic field is produced in a region of interest to align the nuclear spins and a pulsed radio frequency (RF) magnetic field is used to produce spin echo signals indicative of the relaxation properties of the region. Phase modulation of the excitation and/or refocusing pulses is used to reduce the peak and time averaged power requirements over prior art methods that use only amplitude modulation of the RF carrier signal. In an alternate embodiment of the invention, both amplitude and phase modulation are used. The phase may be symmetric or antisymmetric with respect to frequency. In a preferred embodiment of the invention, the phase has a quadratic dependence on frequency.
When used in conjunction with a gradient tool operated at multiple frequencies, the pulse shaping may be used to reduce interference between spin echo signals arising from adjacent volumes of the formation.